Did you already try to remove it and put it back again?
When changing the SIM card, power off the device prior to opening the SIM tray. After you have changed the SIM card for your iPhone you may need to reconnect it to iTunes.
iPhone keeps a record of previously inserted SIM cards, but if the carrier name of your SIM does not show up in the status bar after you changed the SIM you will need to reconnect iPhone to iTunes. If you do not connect iPhone to iTunes after changing or reinserting the SIM, iPhone may not work as expected.
If your iPhone does not show up in iTunes (on the left hand side of the iTunes window under Devices), please see the following links for assistance:
copied from http://support.apple.com/kb/HT2309 About swapping SIM cards
If this does not work, contact your provider, maybe your SIM is damaged.
I am having the same "No SIM card installed" error on an iPhone 4 that I have had for a week. It worked fine, but suddenly this morning it started saying "No SIM card installed". I used it fine on the way to work, but when I got to work, the problem came. I tried removing and reseating the SIM card, but it did not help.
I will be heading to the genius bar after my last class. :-(